1. Field of the Invention
The present invention relates to an electronic azimuth meter for calculating azimuth by detecting magnetic field of the geomagnetism by a magnetic sensor such as a magneto-resistive element.
2. Description of the Prior Art
According to an electronic azimuth meter, there is a concern in which a magnetic field generated at a location of a magnetic sensor is shifted from the magnetic field produced by the geomagnetism owing to the fact that a case of a battery normally comprising stainless steel such as SUS 304, or the like becomes more or less ferromagnetic by cold forming or the like and produces a magnetic field constituting noise in the geomagnetism. There has been a proposal per se for correcting an error by such noise by a correction table or the like (for example, Japanese Patent Laid-Open No. 170663/1998). According to technology proposed by the publication, actually, in order to correct errors in two orthogonal directions X and Y in a horizontal face, with regard to azimuth angle xcex8, a correction calculating equation in the form of cos (2 xcex8) is used and in the case in which the magnetic sensor can be arranged to separate from a battery having an outer shape substantially in a circular plate shape to some degree, the technology is regarded as appropriate qualitatively. Further, it is described in Japanese Patent Laid-Open No. 300869/1994 (Table 1 and FIG. 13 of the publication) that in order to avoid an electronic part which is easy to bear magnetism or magnetize such as a case of a battery from effecting magnetic influence on a magnetic sensor, the electronic part which is easy to bear magnetism or magnetize is made remote from the magnetic sensor and a minimum limit distance which does not effect the magnetic influence is 2 cm (0.02 m) from an edge in the case of, for example, a sliver oxide battery.
However, the inventors have confirmed by experiment that when a case of a main body of an electronic azimuth meter is made as small as possible and a maximum size one is used for a battery, a distance between a magnetic part such as a case of the battery and a magnetic sensor is reduced and in an azimuth in which although a geomagnetic component in X (or Y) direction stays the same, a geomagnetic component in Y (or X) direction differs, an output of an X (or Y)-direction magnetic sensor, that is, a magnetic field detected value in X (or Y) direction by the magnetic sensor, in other words, an X (or Y) direction component of magnetic field formed at a location of the magnetic sensor differs.
The present invention has been carried out in view of the above-described point and it is an object thereof to provide an electronic azimuth meter which is compact and is capable of accurately measuring azimuth and an electronic time piece having the electronic azimuth meter.
In order to achieve the above-described object, according to an aspect of the invention, there is provided an electronic azimuth meter which is an electronic azimuth meter having an electronic azimuth meter main body and X-direction and Y-direction magnetic sensors for detecting magnetic field components of two orthogonal directions of X and Y of the main body, the electronic azimuth meter main body comprising a magnetic part forming at locations of the X-direction and the Y-direction magnetic sensors, magnetic fields Bmx and Bmy by being magnetized by geomagnetism and having components in oblique directions relative to a direction of the geomagnetism specified by magnetic field components Bx and By in an X-Y plane, approximate equation storing means for storing with regard to the respective directions of X and Y, pluralities of approximate equations calculated based on magnetic field detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors with regard to a number of azimuths of the azimuth meter in the geomagnetism having the magnetic field components Bx and By, which are approximate equations (for example, Vxi (Bx, By), Vyj (Bx, By) or Bxi (Vx, Vy), Byj (Vx, Vy)) representing relationships between the detected values Vx and Vy of the magnetic sensors and the magnetic field components Bx and By of the geomagnetism, and azimuth calculating means for calculating the azimuth of the azimuth meter main body by selecting specific approximate equations in the pluralities of approximate equations with regard to the respective directions of X and Y based on the detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors.
According to the electronic azimuth meter of the invention, there are provided xe2x80x9capproximate equation storing means for storing with regard to the respective directions of X and Y, pluralities of approximate equations calculated based on magnetic field detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors with regard to a number of azimuths of the azimuth meter in the geomagnetism having the magnetic field components Bx and By, which are approximate equations (for example, Vxi (Bx, By), Vyj (Bx, By) or Bxi (Vx, Vy), Byj (Vx, Vy)) representing relationships between the detected values Vx and Vy of the magnetic sensors and the magnetic field components Bx and By of the geomagnetism, and azimuth calculating means for calculating the azimuth of the azimuth meter main body by selecting specific approximate equations in the pluralities of approximate equations (for example, Vxi (Bx, By), Vyj (Bx, By) or Bxi (Vx, Vy), Byj (Vx, Vy) with regard to the respective directions of X and Y based on the detected values Vx and Vy of the X-direction and the Y-direction magnetic sensorsxe2x80x9d and therefore, even when there is provided xe2x80x9ca magnetic part forming at locations of the X-direction and the Y-direction magnetic sensors, magnetic fields Bmx and Bmy by being magnetized by geomagnetism and having components in oblique directions relative to a direction of the geomagnetism specified by magnetic field components Bx and By in an X-Y planexe2x80x9d, influence by the magnetic part can be removed, the geomagnetic components of the geomagnetism can be detected and the azimuth of the azimuth meter can be calculated accurately. In this case, in order to calculate accurate azimuth, it is not necessary to know what noise magnetic field is formed by which part.
Therefore, according to the electronic azimuth meter of the invention, the magnetic part can be arranged in a state of being proximate to the magnetic sensor. That is, according to the electronic azimuth meter of the invention, a magnetic part such as a case of a battery typically comprising SUS 304 and easy to include more or less a ferromagnetic phase by a forming step, can be arranged to be proximate to the magnetic sensor and therefore, not only the size of the azimuth meter main body can be minimized but also a battery having a maximum capacity capable of being contained in the case can also be used and the electronic azimuth meter can be made compact and operable for a long period of time.
The electronic azimuth meter is provided with the X-direction and the Y-direction magnetic sensors for detecting respective geomagnetic components in two orthogonal directions of X and Y. The electronic azimuth meter is directed horizontally such that the magnetic field in the horizontal face can be detected by the X-direction and the Y-direction magnetic sensors. In this case, horizontally directing the electronic azimuth meter signifies directing the electronic azimuth meter in directions by which an X-Y plane becomes horizontal and the magnetic sensors detect the magnetic field in the horizontal face.
The magnetic field by the geomagnetism or the geomagnetism Bx, By and Bz differs according to locations on the earth. Strictly speaking, the magnetic field is varied over time. In the case of Japan, at a vicinity of Tokyo, horizontal magnetic force (magnitude of magnetic field (strictly speaking, xe2x80x9cmagnetic flux densityxe2x80x9d) component in a horizontal face of geomagnetism) {(Bx)2+(By)2}xc2xd, is about 30 xcexcT, that is, 30xc3x9710xe2x88x926 T and a direction of the horizontal magnetic force of the geomagnetism is inclined to west by about 6 degree at a vicinity of Tokyo relative to the north direction of the horizontal plane (declination is about 6 degree to west side). Further, dip of the geomagnetism is about 50 degree at a vicinity of Tokyo. Further, in this specification, unless particularly specified otherwise, the term of xe2x80x9cmagnetic fieldxe2x80x9d is used as a definition the same as that of xe2x80x9cmagnetic flux densityxe2x80x9d and the term in the case inherently indicating xe2x80x9cmagnetic flux densityxe2x80x9d is referred to as xe2x80x9cmagnetic fieldxe2x80x9d. In representing the term, not H but B is used.
In this specification, a xe2x80x9cmagnetic partxe2x80x9d is referred to as a part or a portion thereof comprising a material which can be magnetized more than a material of so-to-speak feeble magnetism such as normal paramagnetism or diamagnetism and typically indicates a part partially including a paramagnetic martensitic phase produced by cold-forming SUS 304. Although not so much preferable, naturally, a total of a part may be made of a typical paramagnetic material such as iron, steel or nickel in so-to-speak martensitic phase.
Under the magnetic field by the geomagnetism, a magnetic part is more or less magnetized and magnetic fields Bmx and Bmy produced by magnetizing the magnetic part are superposed on the horizontal magnetic forces Bx and By and magnetic fields Bxa=Vx, Bya=Vy are formed at locations of the X-direction and the Y-direction magnetic sensors. In this case, influence of all the magnetic part is Bmx=Bxaxe2x88x92Bx and Bmy=Byaxe2x88x92By. However, at least any of a spacial distribution of the magnetic part, that is, a position and a shape and a degree of easiness of magnetization (initial magnetic permeability or magnetic susceptibility at a vicinity of zero magnetic field) and the like, is not normally uniform and therefore, when the magnetic part and the magnetic sensor are disposed to be comparatively proximate to each other, even when a geomagnetic component in X (or Y) direction is the same, in an azimuth in which a geomagnetic component in Y (or X) direction differs, an output of an X (or Y)-direction magnetic sensor, that is, a magnetic field detected value Vx (or Vy) in X (or Y) direction by the magnetic sensor, in other words, an X (or Y) direction component Bxa (or Bya) formed at a location of the magnetic sensor differs. Further, although the scope of the invention is not limited, it seems that the direction of the geomagnetism is provided with large dip and therefore, the vertical direction component of the geomagnetism depends on the above-described nonuniformity of the magnetic part and can form the magnetic field in the horizontal face asymmetrical to inversion of the geomagnetism at the location of the magnetic sensor. At any rate, the geomagnetic part is magnetized by the geomagnetism and forms the magnetic fields Bmx and Bmy having components in oblique directions relative to the direction of the geomagnetism specified by the magnetic field components Bx and By in the X-Y plane at locations of the X-direction and the Y-direction magnetic sensors. Therefore, azimuth dependencies of the magnetic field Bmx formed at the location of the X-direction magnetic sensor by the magnetic part and the magnetic field Bmy formed at the location of the Y-direction magnetic sensor, generally differ from each other even when influence of deviation of 90 degree in X and Y directions is removed. However, depending on cases, the dependencies may actually be the same.
As a result, according to the electronic azimuth meter of the invention, even when while changing the azimuth of the azimuth meter, the horizontal magnetic force, that is, the magnetic field detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors are measured in the geomagnetism of the magnetic field components Bx and By and plotted by orthogonal coordinates Bxxe2x88x92Vx or Byxe2x88x92Vy, Vx=Vx (Bx) (or Bx=Bx (Vx)) and Vy=Vy (By) (or By=By (Vy)) are not constituted in a linear shape but in a closed curve shape. Therefore, based on data provided by actual measurement, Vx=Vx (Bx) (or Bx=Bx (Vx)) and Vy=Vy (By) (or By=By (Vy)) are calculated in the form of approximate equations.
According to a first preferable embodiment of the invention, typically, the approximate equations comprise two equations of Vx1 (Bx) and Vx2 (Bx) (or Bx1 (Vx) and Bx2 (Vx)) and Vy1 (By) and Vy2 (By) (or By1 (Vx) and By2 (Vx)) to separately represent an upper half and a lower half of the closed curve by defining i=1, 2 and j=1, 2 such that there are formed one-valued functions in which respectives of Bx and Vx and By and Vy correspond to each other in a one-to-one relationship. Naturally, when the influence of the noise magnetic fields Bmx and Bmy by the magnetic part is significant and is complicatedly dependent upon the azimuth, with regard to at least one of them, the approximate equation may be divided into three or more areas and approximate equations of the respective areas may be calculated.
Meanwhile, according to a second preferable embodiment of the invention, based on new knowledge that the above-described closed curve can be represented by the form of Bx=Bx[cos{xcex2x(xcex1x(Vx))+xcex4x}] and By=By[sin{xcex2y(xcex1y(Vy))+xcex4y}], approximate equations are calculated. Further, xcex2x(xcex1x(Vx)) and xcex2y(xcex1y(Vy)) are divided into a plurality of areas in accordance with a relationship provided by xcex2x with regard to the maximum value VxM and the minimum value Vxm of the magnetic field detected value Vx of the X-direction magnetic sensor as well as a relationship provided by xcex2y with regard to the maximum value VyM and the minimum value Vym of the magnetic field detected value Vy of the Y-direction magnetic sensor and are represented by relationships in the respective areas. With regard to the second embodiment, a summarized explanation will later be given and in the following, an explanation will be given of characteristics common to the first and the second embodiments and characteristics with regard to the first embodiment.
In the case in which the horizontal magnetic forces Bx and By are calculated from the detected values Vx and Vy of the magnetic sensors, when predetermined approximate equations are selected from pluralities of approximate equations with regard to respective directions of X and Y, the approximate equations are selected in accordance with division or section references for dividing pluralities of approximate sections or approximate areas. In dividing the approximate areas, typically, with regard to the respectives of the X direction and the Y direction, a direction or an azimuth maximizing or minimizing a detected output constitutes a boundary of division.
According to the first embodiment, with regard to the boundary, approximately, in respect of Vx, typically, locations where the azimuth is 0 degree (direction in which direction of horizontal magnetic force and X direction coincide with each other) and 180 degree (direction in which direction of horizontal magnetic force and X direction are opposed to each other) constitute boundaries and in respect of Vy, typically, locations where the azimuth is 90 degree (direction in which direction of horizontal magnetic force and Y direction coincide with each other) and 270 degree (direction in which direction of horizontal magnetic force and Y direction are opposed to each other) constitute the boundaries. Therefore, the approximate areas are partitioned typically at locations of four azimuths of east, west, south and north of the geomagnetism. That is, with regard to one direction of the X direction and the Y direction, the approximate area is divided by north azimuth (0 degree) and south azimuth (180 degree) and with regard to other direction, the approximate area is divided by west (90 degree) and east (270 degree).
According to the specification, unless not particularly specified otherwise, the azimuth or the azimuth angle is represented by notation xcfx86 and is represented such that north is 0 degree, west is 90 degree, south is 180 degree and east is 270 degree. With regard to geographical xe2x80x9cazimuth anglexe2x80x9d, the angle is represented by notation xcex8 and is described as display azimuth angle. Further, xcfx86+xcex8=360xc2x0.
Further, generally, although Vx and Vy depend both of Bx and By in the form of Vx=Vx (Bx, By) and Vy=Vy (Bx, By), as mentioned above, Bx and By designate two components of the horizontal magnetic force having a constant magnitude in the same district and accordingly, Bx and By can be determined in the form of Bx=Bx (By) or By=By (Bx) and accordingly, so far as used in the same district, Vx and Vy can be represented as Vx=Vx (Bx) and Vy=Vy (By) without losing generality. When desired, Vx and Vy may be represented in the form of Vx=Vx (By) and Vy=Vy (Bx).
The respective approximate equation is actually a curve and accordingly, when the respective approximate equation is approximated by a polynomial, the respective approximate equation becomes a second or higher degree equation. The inventors have confirmed as exemplified later in the first embodiment, that an approximate equation having sufficient accuracy can be provided by being approximated by a second degree equation. For example, when each of Vx (Bx) and Vy (By) is divided in two areas and approximated by second degree polynomials, a minimum of three points of data may be provided at each area. When two points in the three points are constituted by points of boundaries of an area, the two points can commonly be used in two areas and therefore, with regard to each area, only data of one point at middle may be provided. That is, when each of Vx (Bx) and Vy (By) is divided into two areas and is approximated by second degree equations, with regard to respectives of Vx (Bx) and Vy (By), data of four points may be provided.
According to the first embodiment, for example, when the approximate equation is divided into two areas in each of the X direction and the Y direction, with regard to the X direction, the approximate equation is divided into a range of azimuth angle of 0 degree-90 degree-180 degree and a range of 180 degree-270 degree-360 degree (0 degree) and with regard to the Y direction, the approximate equation is divided into a range of azimuth angle of 90 degree-180 degree-270 degree and a range of 270 degree-360 degree (0 degree)-90 degree. With regard to way of approximation, for example, (1) in respect of Vx (Bx), there are calculated a first X-direction quadratic equation Vx1 (Bx) where the azimuth angle passes through three points of 0 degree, 90 degree and 180 degree and a second X-direction quadratic equation Vx2 (Bx) where the azimuth angle passes through three points of 180 degree, 270 degree and 0 degree (360 degree), with regard to a middle azimuth, the azimuth is approximated by the first or the second X-direction quadratic equation Vxi (Bx) (where i=1, 2) and with regard to Vy (By), there are calculated a first Y-direction quadratic equation Vy1 (By) where the azimuth angle passes through three points of 90 degree, 180 degree and 270 degree and a second Y-direction quadratic equation Vy2 (By) where the azimuth angle passes through three points of 270 degree, 0 degree (360 degree) and 90 degree and with regard to a middle azimuth, the azimuth may be approximated by the first or the second quadratic equation Vyj (By) (where j=1, 2), or (2) quadratic equations may be calculated by the least squares method by using four or more azimuths, that is, measured values of four points or more in the above-described respective ranges, or (3) approximate equations in the respective angular ranges may be calculated by Lagrangean approximation method, that is, Lagrangean interpolation polynomial. When the Lagrangean approximation method is used, (3-a) within the respective ranges, quadratic polynomials may be derived as approximate equations by using three points of both ends and middle or (3-b) polynomials passing through N of desired measured points of four points or more in respective ranges may be derived as approximate equations. In the case of (3-a), the approximate equations coincide with the above-described polynomials of (1). Further, when desired, approximate equations may be approximated by equations other than polynomials.
In this way, according to the first embodiment, for example, with regard to Vy (By), approximate equations are calculated in the form of Vy1=Ay1xc2x7By2+Cy1xc2x7By+Dy1 and Vy2=Ay2xc2x7By2+Cy2xc2x7By+Dy2 (where Ay1, Ay2, Cy1, Cy2, Dy1 and Dy2 are constants) and also with regard to Vx1, Vx2, approximate equations are calculated in the form of Vx1=Ax1xc2x7Bx2+Cx1xc2x7Bx+Dx1 and Vx2=Ax2xc2x7By2+Cx2xc2x7By+Dx2 (where Ax1, Ax2, Cx1, Cx2, Dx1 and Dx2 are constants).
According to the first embodiment, in the case of calculating the approximate equations in the form of (1) or (2), mentioned above, approximate equation storing means is stored with pluralities of such approximate equation Vxi (Bx, By) typically, Vxi (Bx), Vyj (Bx, By), typically, Vyj (By) and notations i and j designate integers of 2 or more. Further, actually, to easily utilize the approximate equations, approximate equation Vxi (Bx) is stored in an inversely converted form of Bx=Bxi (Vx) and approximate equation Vyj (By) is stored in an inversely converted form of By=Byj (Vy). However, also in this case, when desired, from the start, approximate equation may be calculated in the form of By=Byj (Vy).
More generally, the approximate equations between the magnetic field components Bx and By and the magnetic field detected values Vx and Vy stays to be equivalent both in the form of Vxi (Bx, By) and Vyj (Bx, By) and in the form of Bxi (Vx, Vy) and Byj (Vx, Vy) and in this specification, the statement xe2x80x9capproximate equations Vxi (Bx, By) and Vyj (Bx, By) calculated based on the magnetic field detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors with regard to a number of azimuths of the azimuth meter in the geomagnetism of the magnetic field components Bx and By, which are the approximate equations Vxi (Bx, By) and Vyj (Bx, By) representing relationships between the detected values Vx and Vy of the magnetic sensor and the magnetic field components Bx and By of the geomagnetismxe2x80x9d, signifies to include xe2x80x9cthe approximate equations Bxi (Vx, Vy) and Byj (Vx, Vy) calculated based on the magnetic field detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors with regard to a number of azimuths of the azimuth meter in the geomagnetism of the magnetic field components Bx and By, which are the approximate equations Bxi (Vx, Vy) and Byj (Vx, Vy) representing relationships between the detected values Vx and Vy of the magnetic sensor and the magnetic field components Bx and By of the geomagnetismxe2x80x9d except a case particularly mentioned specifically.
In the first embodiment, in the case of using an approximation method such as Lagrangean approximation method, when the approximation equation is calculated in the form of, for example, Bx=Bxi (Vx) from the start, the following relationship is established.
Bxi=BxkFvxk 
where, for simplifying symbols, with regard to a subscript k, cyclically, a sum of k=m through n is calculated and a lower limit m and an upper limit n of k are determined in accordance with an approximate area i.
In the above equation, the following is established.
Fvxk=II(Vxxe2x88x92Vxp)/(Vxkxe2x88x92Vxp) 
where with regard to a subscript p, a product of from m to n is cyclically calculated except p=k.
Also with regard to Byj, the following relationship is similarly established.
Byj=BykFvyk 
where with regard to the subscript k, a sum of k=m through n is cyclically calculated and the lower limit m and the upper limit n of k are determined in accordance with an approximate area j. In the above equation, the following is established.
Fvyk=II(Vyxe2x88x92Vyp)/(Vykxe2x88x92Vyp) 
where with regard to the subscript p, a product from m to n is cyclically calculated except p=k.
That is, in the first embodiment, when Lagrangean approximation method is used, the approximate equation storing means comprises a storing unit of the general approximate equations and values (Bxk, Vxk) and (Byk, Vyk) which are to be taken in the respective areas. Naturally, in the case of data which are to be used commonly at contiguous ares such as boundary values, a side of selecting the data may be determined and one common data may be stored. For example, in the case of using data with regard to four azimuths of east, west, south and north of the geomagnetism, (Bxk, Vxk) and (Byk, Vyk) with regard to the four azimuths and Lagrangean interpolation polynomials in the X direction and the Y direction and information of the range k may be stored.
Meanwhile, as a result of carrying out further experimental verification and analysis with regard to the Bxxe2x88x92Vx characteristic and the Byxe2x88x92Vy characteristic, the inventors have found approximate equations more accurately reflecting influence by the noise magnetic field Bm and capable of accurately carrying out calibration. That is, the inventors have found that an X-direction magnetic field measured value Vx=Vx{xcfx86} and a Y-direction magnetic field measured value Vy=Vy{xcfx86} are provided with two characteristics (1) and (2), mentioned below, by gross classification.
(1) Azimuth angle dependency Vxxcex3Vx{xcfx86} of the X-direction magnetic field detected value Vx is shifted from cosine curve with regard to the azimuth angle xcfx86 in its phase by xcex4x ( less than 0) and the azimuth angle dependency Vy=Vy{xcfx86} of the Y-direction magnetic field detected Vy is shifted from sine curve with regard to the azimuth angle xcfx86 in its phase by xcex4y ( greater than 0). In other words, Vx=Vx{xcfx86} actually coincides with the cosine curve except that the phase is shifted by xcex4x ( less than 0) and Vy=Vy{xcfx86} actually coincides with the sine curve except that the phase is shifted by xcex4y ( greater than 0). It seems that positive or negative (of directions) and magnitudes of the phase shifts xcex4x and xcex4y depend mainly on relative positions of the X-direction and the Y-direction sensors 21 and 22 relative to the battery that is, directions and distances.
(2) When a battery having a different spontaneously magnetized state (magnetism bearing state) is contained, in the case of removing the influence of shift by respectively normalizing (for example, maximum value is +1 and minimum value is xe2x88x921) Vx=Vx{xcfx86} and Vy=Vy{xcfx86} by which Vx (ordinate)-Bx (abscissa) characteristic and Vy (ordinate)-By (abscissa) characteristic indicate different shifts (deviation) in the ordinate directions Vx and Vy even when the battery is interchanged or a direction (rotational portion) of a button type battery in a circular disk shape is changed, actually, xcex4x and xcex4y do not change significantly but are maintained substantially constant.
By presence of the shifts of the phase angles or the phase difference xcex4x and xcex4y, the azimuth angle xcfx86 deviates from the directions of 0xc2x0, 90xc2x0, 180xc2x0 and 270xc2x0 even when directions in which the magnetic field detected values Vx and y take maximum values Vxm and Vym and minimum values Vxm and Vym. The directions include errors from the start when initial setting or calibration is carried out by implicitly assuming that xe2x80x9cthe directions in which the magnetic field detected values Vx and Vy become the maximum values Vxm and Vym and the minimum values Vxm and Vym, coincide with directions in which the azimuth angle xcfx86 become 0 degree, 90 degree, 180 degree and 270 degreexe2x80x9d. The errors become significant with regard to the magnetic field detected values at vicinities of azimuths where the geomagnetic components become null such that vicinities of Vy{0}, Vx{90}, Vy{180} and Vx{270} at which dVx/dxcfx86 and dVy/dxcfx86 become large rather than vicinities of the maximum values and the minimum values of Vx and Vy. Therefore, when the influence of the phase shifts xcex4x and xcex4y is removed, more accurate azimuths can be measured.
In the case of considering the phase differences or the phase shifts xcex4x and xcex4y, the approximate equations are generally given as follows.
Bxn=cos xcfx86=cos(xcex2x+xcex4x)xe2x80x83xe2x80x83Equation (1) 
Byn=sin xcfx86=sin(xcex2y+xcex4y)xe2x80x83xe2x80x83Equation (2) 
In the above equations, xcex2x and xcex2y are xcex2x=xcfx86xe2x88x92xcex4x and xcex2y=xcfx86xe2x88x92xcex4y with regard to the azimuth angle xcfx86 and Bxn and Byn represent the magnetic field components Bx and By of the geomagnetism in the X and the Y directions in which the amplitude is normalized to 1.
Also Vx and Vy are represented as follows by taking amounts Vxn and Vyn where the amplitudes are normalized to 1.
Vxn=cos(ax)xe2x80x83xe2x80x83Equation (7A) 
Vyn=cos(ay)xe2x80x83xe2x80x83Equation (8A) 
magneto-resistive (MR) element is used, so far as a magnetic field of a horizontal magnetic force component of the geomagnetism of about 1 xcexcT can be detected, in place thereof, a giant magnetic resistive effect (GMR) element or any transducer for converting a magnetic (magnetic field) signal into other physical amount such as an electric signal, an optical signal or other magnetic signal of a magnetized state may be used. As the magneto-resistive element, for example, an element described in U.S. Pat. No. 5,521,501 is preferable. The X-direction magnetic sensor and the Y-direction magnetic sensor typically arranged to be proximate to each other such that for example, substantially an L-like shape is constituted as a whole in consideration of efficient formation of arrangement space, power feed line and signal line. However, depending on cases, the X-direction magnetic sensor and the Y-direction magnetic sensor may be arranged at separate locations. For example, in the case of using a battery having a plane shape of substantially a circular shape or an elliptical shape, the X-direction magnetic sensor and the Y-direction magnetic sensor may separately be arranged along two orthogonal symmetric center lines of the battery.
Further, xcex4x and xcex4y are calculated as follows as amounts inherent to the electronic azimuth meter which are not actually dependent upon interchange of the battery in ranges to some degree from measured data with regard to four azimuths.
xcex4x=arctan[(Vxn{90}xe2x88x92Vxn{270})/Vxn{0}xe2x88x92Vxn{180})]xe2x80x83xe2x80x83Equation (16) 
xcex4y=arctan[xe2x88x92Vyn{0}xe2x88x92Vyn{180})/Vyn{90}xe2x88x92Vyn{270})]xe2x80x83xe2x80x83Equation (17) 
In this case, when there actually are no offsets in Vx and Vy, xcex4x and xcex4y may be calculated from two azimuth data in place of four azimuth data.
Therefore, according to the second embodiment of the invention, azimuth calculating means is constituted such that a large or small relationship between a detected value of one magnetic sensor in the X-direction and the Y-direction magnetic sensors and a first reference value, is compared and based on a result of the comparison, approximate equation in a plurality of approximate equations is selected with regard to other magnetic sensor in the X-direction and the Y-direction magnetic sensors, based on the approximate equation, the magnetic field component in a corresponding direction of the geomagnetism is calculated, a large or small relationship between the magnetic field component or the detected value of the one magnetic sensor and a second reference value, is compared and based on a result of the comparison, the approximate equation in the plurality of approximate equations is selected with regard to the one magnetic sensor. In this case, the approximate equations become plural since when the above-described Equation (7A) and Equation (8A) are represented as equations with regard to xcex1x and xcex1y in order to provide the relationship between xcex2x and xcex1x and the relationship between xcex2y and xcex1y, many-valued functions are constituted.
However, in the case of the second embodiment, with regard to respectives of the X direction and the Y direction, it is known that the approximate equations can be represented finally by a single cosine function and a single sine function and therefore, way of calculating azimuth may be changed from the above-described procedure.
Further, according to the second embodiment of the invention, approximate equation storing means is provided with a phase difference data storing portion for storing the phase difference data xcex4x and xcex4y in the X direction and the Y direction calculated from the magnetic field detected values of the X-direction and the Y-direction magnetic sensors with regard to four azimuths of east, west, south and north of the geomagnetism and the approximate equations in the X direction and the Y direction comprise cosine function and sine function respectively including xcex4x and xcex4y.
Further, according to the second embodiment of the invention, approximate equation storing means is provided with a maximum and minimum data storing portion for storing the maximum values VxM and VyM and the minimum values Vxm and Vym of the magnetic field detected values of the X-direction and the Y-direction magnetic sensors, the approximate equations in the X direction are specified by the maximum value VxM and the minimum value Vxm of the magnetic field detected values of the X-direction magnetic sensor and the phase difference xcex4x in the X direction and the approximate equation in the Y direction is specified by the maximum value VyM and the minimum value Vym of the magnetic field detected values of the Y-direction magnetic sensor and the phase difference xcex4y in the Y direction.
Approximate equation storing means typically comprises a non-volatile memory, for example, EEPROM. When the magnetic part is exposed to a magnetic field sufficiently stronger than the geomagnetism or exposed under a magnetic field in the same direction for a long period of time, the magnetized state or the magnetism bearing state including a magnetic domain state of a ferromagnetic phase area, is changed and therefore, the approximate equations may be subjected to a processing of recalculation as desired, that is, calibration or updating of the azimuth meter may be carried out. Particularly, in the case of interchanging the battery, the magnetic properties of the case can be changed owing to a history of fabricating the case made of stainless steel of the battery and therefore, when interchanging the battery, calibration may be carried out. The calibration may be carried out by the user or a predetermined supply source of the electronic azimuth meter.
In order to enable calibration or updating at least by the user, in the first embodiment, the approximate equation storing means of the electronic azimuth meter is provided with a four azimuth data storing portion for storing the magnetic field detected values of the X-direction and the Y-direction magnetic sensors with regard four azimuths of east, west, south and north of the geomagnetism and the electronic azimuth meter is provided with updating means for updating the magnetic field detected values of the four azimuths of east, west, south and north of the geomagnetism stored to the four azimuth data storing portion and approximate equation calculating means for calculating the approximate equations Vxi (Bx) and Vyj (By) in the X-direction and the Y-direction based on the magnetic field detected values of the four azimuths of east, west, south and north of the geomagnetism stored to the four azimuth data storing portion. At every time of updating the four azimuth data, based on the updated data, the approximate equations are recalculated by the approximate equation calculating means and newly provided approximate equations are stored to the approximate equation storing means.
Meanwhile, in the case of the second embodiment, in order to enable to carry out calibration or updating at least by the user, there may be provided updating means for updating maximum values and minimum values of the X-direction and the Y-direction magnetic field detected values stored to the maximum and the minimum data storing portion.
When the electronic azimuth meter is brought into the horizontal state and is directed to a desired azimuth at a desired location, by the horizontal magnetic forces Bx and By of the geomagnetism in accordance with the azimuth, respectives of the X-direction and the Y-direction magnetic sensors provide outputs Vx and Vy in accordance with the magnetic field formed at the magnetic sensors.
Based on the outputs Vx and Vy, the azimuth calculating means determines one approximate equation to be used from the pluralities of approximate equations Vxi and Vyj for each of the X-direction and the Y-direction magnetic sensors.
Further particularly, in the case of the first embodiment, according to the azimuth calculating means, for example, a large or small relationship between a detected value (for example, Vx) of one (for example, X-direction) magnetic sensor in the X-direction and the Y-direction magnetic sensors and the first reference value, is compared, based on a result of the comparison, one approximate equation in the plurality of approximate equations is selected with regard to other (for example, Y-direction) magnetic sensor of the X-direction and the Y-direction magnetic sensors, based on the approximate equation, the magnetic component (for example, By) in a corresponding direction of the geomagnetism is calculated, a large or small relationship between the magnetic field component and the second reference value is compared and based on a result of the comparison, one approximate equation in the plurality of equations is selected with regard to the one magnetic sensor.
That is, for example, when the approximate equations are two of respectives of Vx1 and Vx2 and Vy1 and Vy2 as mentioned above and as four points, four points of 0 degree, 90 degree, 180 degree and 270 degree are adopted for the azimuth angle xcfx86, by using values of Vx (Bxxe2x88x92max) and Vx (Bxxe2x88x92min) in the case of the azimuth angles of xcfx86 of 0 degree and 180 degree (in the following, with the azimuth angle as a variable in place of the magnetic field, these are also represented as Vx{0} and Vx{180}), {Vx(Bxxe2x88x92max)+Vx(Bxxe2x88x92min)}/2 constitutes the first reference value, the first reference value is compared with Vx, when Vx is larger, the azimuth angle xcfx86 is to be disposed in a range of xe2x88x9290 degree (270 degree)-0 degree (360 degree)-90 degree and therefore, with regard to Vyj (By), there is selected the approximate equation Vy1 (By) covering the range from xe2x88x9290 degree (270 degree) to 90 degree, conversely, when Vx is smaller, the azimuth angle xcfx86 is to be disposed in the range of 90 degree-180 degree-270 degree and accordingly, with regard to Vyj (By), there is selected the approximate equation Vy2 (By) covering the range of 90 degree through 270 degree. Further, in the case in which by influence of shape or arrangement of the magnetic part and the vertical direction component of the geomagnetism, the azimuth of the electronic azimuth meter is inverted, when way of change of the magnetic field in accordance with change of the azimuth angle significantly differs, the first reference value may be determined in consideration of the characteristic.
Next, from the selected approximate equation Vy1 (By) or Vy2 (By) (more in details, typically, approximate equation in an inversely-converted form) and the measured value Vy, the magnetic field component By of the horizontal magnetic force of the geomagnetism is calculated, zero is adopted as the second reference value, and when the magnetic field component By is positive, azimuth angle xcfx86 is to be disposed in the range of 0 degree-90 degree-180 degree and accordingly, with regard to Vxi (Bx), there is selected the approximate equation Vx1 (Bx) covering the range of 0 degree through 180 degree and when the magnetic field component By is negative, the azimuth angle xcfx86 is to be disposed in the range of 180 degree-270 degree-360 degree (0 degree) and accordingly, with regard to Vxi (Bx), there is selected the approximate equation Vx2 (Bx) covering the range of 180 degree through 360 degree. Further, based on the selected approximate equation (more in details, typically, approximate equation in the inversely-converted form), the magnetic field component Bx of the horizontal magnetic force of the geomagnetism is calculated.
Meanwhile, in the case of the second embodiment, as mentioned above, the azimuth calculating means is constituted such that the large or small relationship between the detected value of one magnetic sensor of the X-direction and the Y-direction magnetic sensors and the first reference value is compared and based on the result of comparison, with regard to other magnetic sensor of the X-direction and the Y-direction magnetic sensors, one approximate equation of the plurality of approximate equations is selected, the magnetic field component in the corresponding direction of the geomagnetism is calculated based on the approximate equation, the large or small relationship between the magnetic field component or the detected value of the one magnetic sensor and the second reference value is compared and based on a result of the comparison, with regard to the one magnetic sensor, one approximate equation of the plurality of approximate equations is selected.
Azimuth angle xcfx86 is calculated in the form of arctan (By/Bx) from the magnetic field components Bx and By calculated in this way and the azimuth is calculated. Further, arctan is also typically calculated by using a polynomial having fast convergence as approximate equation.
That is, based on the detected values Vx and Vy of the X-direction and the Y-direction magnetic sensors, the azimuth calculating means calculates the X-direction and the Y-direction components Bx and By of the horizontal magnetic force of the geomagnetism and calculates the azimuth of the azimuth meter.
The electronic azimuth meter main body is basically of any shape and typically, a plane shape thereof is substantially a rectangular shape or a rectangular shape in a square shape, substantially a circular shape or substantially an elliptical shape. Naturally, strictly speaking, there are many cases in which the plane shape is a further complicated shape. Further, in this specification, a substantially rectangular shape signifies to include a polygonal shape in which with a substantially rectangular shape or a substantially square shape as basis, at least a portion of a side is constituted by a plurality of sides. Further, a number of the magnetic parts, positions and shapes thereof may basically of any of them.
In order to make the electronic azimuth meter main body as compact as possible and operable for a long period of time, according to the electronic azimuth meter main body, typically, the plane shape is substantially a rectangular shape, that is, a shape substantially near to a square shape or a rectangular shape, there is arranged a battery in a circular disk shape or a circular plate shape which is large to a degree of equal to be inscribed substantially to a rectangular shape in consideration of arrangement of other parts at a central portion of the electronic azimuth meter main body and the magnetic sensors are arranged at a location where a gap is produced between a rectangular shape and a circle inscribed to the rectangular shape by an extreme expression, that is, a corner of the rectangular shape. Further, an existing small-sized thin type battery is provided with a plane shape substantially in a circular shape and accordingly, in order to minimize the size of the main body, the plane shape of the electronic azimuth meter main body is constituted by substantially a rectangular shape, however, when the plane shape of the thin type battery is provided with a shape other than the circular shape, the plane shape of the electronic azimuth meter main body can be changed in accordance therewith.
When the electronic azimuth meter main body, more in details, the case is substantially rectangular, typically, the magnetic field directions X and Y detected by the above-described X-direction and Y-direction magnetic sensors are selected to coincide with directions of extending two sides of the rectangular shape. Further, when desired, the directions of extending two sides of the rectangular shape may differ from the X and the Y direction. For example, in view of an X-Y plane, a direction along a line connecting a position in correspondence with the center of the circular battery and the magnetic sensor may constitute the X direction or the Y direction.
Although as the magnetic sensor, for example, a magneto-resistive (MR) element is used, so far as a magnetic field of a horizontal magnetic force component of the geomagnetism of about 1 ?T can be detected, in place thereof, a gigantic magnetic resistive effect (GMR) element or any transducer for converting a magnetic (magnetic field) signal into other physical amount such as an electric signal, an optical signal or other magnetic signal of a magnetized state may be used. As the magneto-resistive element, for example, an element described in U.S. Pat. No. 5,521,501 is preferable. The X-direction magnetic sensor and the Y-direction magnetic sensor are typically arranged to be proximate to each other such that for example, substantially an L-like shape is constituted as a whole in consideration of efficient formation of arrangement space, power feed line and signal line. However, depending on cases, the X-direction magnetic sensor and the Y-direction magnetic sensor may be arranged at separate locations. For example, in the case of using a battery having a plane shape of substantially a circular shape or an elliptical shape, the X-direction magnetic sensor and the Y-direction magnetic sensor may separately be arranged along two orthogonal symmetric center lines of the battery.
The above-described electronic azimuth meter can adopt a mode of an electronic time piece having an electronic azimuth meter (or electronic azimuth meter having electronic timepiece) in which there are selected a mode of operating as an azimuth meter by a mode selecting switch such as a push button switch and a mode operating as a time piece by being assembled to a case integrally with an electronic time piece such as a wrist watch.